There are thousands of stocks on the market. Warren Buffett owns very few of them. Most of his fortune is tied up in Berkshire Hathaway (NYSE:BRK.A) (NYSE:BRK.B) stock. And while Berkshire invests in publicly traded companies, its portfolio includes only around 40 stocks.

Buffett doesn't personally pick all of Berkshire's investments these days, but he's still actively involved in the decision-making process. Here are three stocks that the Oracle of Omaha probably won't buy or approve buying. But they belong on your list to consider.

Warren Buffett with people in background

Image source: The Motley Fool.

1. Alphabet

Shoulda, woulda, coulda. That's the story for Warren Buffett and Alphabet (NASDAQ:GOOG) (NASDAQ:GOOGL). Buffett told Berkshire shareholders in 2017 that he should have bought shares of the Google parent years ago but didn't. He's leery of the stock now because of technological uncertainty that Alphabet faces.

Don't get too hung up on Buffett's reluctance to buy Alphabet stock now, though. While every tech company deals with uncertainty, there are quite a few certainties that make Alphabet attractive.

For one thing, Alphabet's moat is rock-solid. No rival is going to dethrone the company's position among search engines, the area where it makes most of its money. Another certainty for Alphabet is that it will have plenty of cash to invest in keeping up with technological advances. The company reported nearly $120 billion in cash, cash equivalents, and marketable securities at the end of the first quarter.

Even some of the fronts that are less certain for Alphabet are still very promising. Its Google Cloud business still ranks only in third place in the cloud hosting market but is growing fast. No one knows how long it will take for self-driving cars to become widely adopted, but there's a really good chance that Alphabet's Waymo will be a major player in the market when it happens.

What about the uncertainty related to the COVID-19 pandemic? Alphabet should be able to weather the storm relatively well based on its Q1 results.

2. Innovative Industrial Properties

Buffett joked some about marijuana in his comments at the annual Berkshire Hathaway shareholders meeting last weekend. But it's highly unlikely the billionaire investor will opt to buy any marijuana stocks. If he did, though, my vote would be for Innovative Industrial Properties (NYSE:IIPR) to be at the top of his list. 

Innovative Industrial Properties (IIP) ranks as the leading real estate investment trust (REIT) focused on the medical cannabis market. The company's business model focuses primarily on sale-leaseback deals, where it buys a property from a medical cannabis operator then leases the property back to the customer. Both sides win. The customer gets an influx of cash, while IIP gets a long-term revenue stream.

This business model has proven to be quite successful for IIP. The company's revenue and profits have skyrocketed in recent years. There should also be plenty of opportunities for IIP to grow in the future with markets expanding in the 33 states where medical cannabis is already legal and more states potentially on the way to legalize medical cannabis later this year.

IIP is a rarity in the cannabis industry in that it pays a dividend. The company's dividend yield currently stands at a little over 5%. With the prospects for more earnings growth, it's a pretty good bet that more dividend hikes are in store.

3. Livongo Health

If you check out Berkshire Hathaway's investment portfolio, you'll find that it's mainly loaded with large-cap stocks. While Berkshire owns a handful of smaller stocks, Livongo Health (NASDAQ:LVGO) might fly beneath Buffett's radar with its market cap below $5 billion. But I don't think Livongo will be this small for much longer.

Unlike Alphabet and Innovative Industrial Properties (and Berkshire itself, for that matter), Livongo has been a huge winner so far in 2020. The company's technology that helps individuals managed chronic conditions more effectively has been a big hit with employers and payers looking for ways to keep healthcare costs under control. Livongo's customer base now includes more than 30% of the Fortune 500. 

Livongo initially focused only on diabetes management. Now, though, the company is also targeting hypertension and sees opportunities for using its technology to assist patients with behavioral health issues and help individuals manage their weight. Diabetes and hypertension by themselves present a huge potential market of close to $47 billion per year.  

The main negative for Livongo Health is that it isn't profitable yet. However, with the tremendous growth runway and an attractive subscription-based model, I think it's only a matter of time before the company will begin to deliver solid profits. And maybe, just maybe, Livongo will be big enough in the near future to catch the eye of a certain investing legend in Nebraska.